Servizio Comunitario di Informazione in materia di Ricerca e Sviluppo - CORDIS

Reasoning with partially ordered information

In many applications, the reliability relation associated with available information is only partially defined, while most of existing uncertainty frameworks deal with totally ordered pieces of knowledge. Partial pre-orders offer more flexibility than total pre-orders to represent incomplete knowledge. Moreover, they avoid comparing unrelated pieces of information.

Possibilistic logic, which is an extension of classical logic, deals with totally ordered information. It offers a natural qualitative framework for handling uncertain information. Priorities are encoded by means of weighted formulas, where weights are lower bounds of necessity measures.

We have proposed, in the framework of the REVIGIS project, an extension of possibilistic logic when pieces of information are only partially ordered. We have first proposed a natural definition of the possibilistic logic inference based on the family of totally ordered knowledge bases (resp. possibility distributions), which are compatible with a partial knowledge base. Then we provided a semantic (resp. syntactic) characterization of this inference, which is based on a strict partial order on interpretations (resp. on a strict partial order on consistent sub-bases of the knowledge base).

Then, we have shown that the main properties of the possibilistic logic (subsumed formulas, clausal form, soundness and completeness results) holds for a partially ordered knowledge base. Finally, we have proposed an algorithm for computing the set of plausible conclusions of a partially ordered knowledge base. We also generalized several iterated revision methods, defined for totally ordered information, to the case of partially ordered information, according to a semantic and a syntactic point of view, and we showed the equivalence between semantic and syntactic approaches.

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83957 LA GARDE